Sure! I see that coordination stuff happening down there. It's Robin that's with Lobsang now, so wouldn't sticking to an encountered Batman would be normal? Although depending on how things play, Lobsang might want to try and find Tim while he's in Gotham again. There isn't much to draw him home yet.
Nothing that I know of. He could distract Hiro, maybe. Speaking of whom. ... I should do something about that.
For whenever and however we send the local Batman away: I think he might not want it advertised that he's gone, but at least let some of the imported heroes know over the network (Batgirl could maybe pass the message?) that he's gonna be away for a while. So over the computers, the event might be kind of quiet? Unless BatB Batman focuses that attention by existing. ... I'm not sure if I had a point in there or not, but it's gone now.